# BPS District Mathematics Standards Book

### K-8 Grade Levels

#### Grade 04

**Fourth Grade Math "I can ... statements"**

In 4th grade, your child will gain important new skills while continuing to build on what he or she learned the previous year. One of the main areas studied in 4th grade is arithmetic and applying it to solve problems. This is an important life skill, and your child should make significant strides in this area during the year. Your child will also build knowledge and skills with fractions to prepare for mastering this topic in 5th and 6th grades. These skills will help ensure your child is ready for algebra and advanced math.

**MAT-04.OA** Domain:

**[OA] Operations and Algebraic Thinking**

**MAT-04.OA.01**Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.**MAT-04.OA.02**Use drawings and equations with a symbol for the unknown number (variable) to represent the problem. Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.**MAT-04.OA.03**Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown**MAT-04.OA.04**Find all factor pairs for a whole number in the range 1-36. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-36 is a multiple of a given one-digit number or is prime or composite.**MAT-04.OA.05**Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

**MAT-04.NBT** Domain:

**[NBT] Number and Operations in Base Ten**

**MAT-04.NBT.01**Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right**MAT-04.NBT.02**Read and write multi-digit whole numbers to the one millions place using base-ten numerals, word form, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of c**MAT-04.NBT.03**Use place value and/or understanding of numbers to round multi-digit whole numbers to any place.**MAT-04.NBT.04**Fluently add and subtract multi-digit whole numbers to the one millions place using strategies flexibly, including the standard algorithm.**MAT-04.NBT.05**Using strategies based on place value and the properties of operations, multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers. Illustrate and Explain the calculation by using equations, rectangular arrays, and/or area models**MAT-04.NBT.06**Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and Explain the calculation by using equations, rectangular arrays, and/or area models.

**MAT-04.NF** Domain:

**[NF] Number and Operations Fractions**

**MAT-04.NF.01**Using visual fraction models, explain why a fraction a/b is equivalent to a fraction (n X a)/(n X b). Use this principle to recognize and generate equivalent fractions.**MAT-04.NF.02**By creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2, compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the**MAT-04.NF.03**- Understand a fraction a/b with a > 1 as a sum of unit fractions 1/b.- MAT-04.NF.03.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- MAT-04.NF.03.b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation. Justify decompositions by using a visual fraction model or other strategies.
- MAT-04.NF.03.c Add and subtract mixed numbers with like denominators.
- MAT-04.NF.03.d Using visual fraction models and equations, solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

**MAT-04.NF.04**- Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.- MAT-04.NF.04.a Understand a fraction a/b as a multiple of 1/b.
- MAT-04.NF.04.b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number
- MAT-04.NF.04.c Using visual fraction models and equations, solve word problems involving multiplication of a fraction by a whole number.

**MAT-04.NF.05**Express a fraction with denominator 10 as an equivalent fraction with denominator 100. Use this technique to add two fractions with respective denominators 10 and 100.**MAT-04.NF.06**Use decimal notation for fractions with denominators 10 or 100.**MAT-04.NF.07**- Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

### MAT-04.MD Domain:

**MAT-04.MD.01**Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.**MAT-04.MD.02**Use the four operations to solve word problems involving distances, time intervals, liquid volumes, objects masses, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Using diagrams such as number line diagrams that feature a measurement scale, to represent measurement quantities**MAT-04.MD.03**Apply the area and perimeter formulas for rectangles in real world and mathematical problems**MAT-04.MD.04**Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.**MAT-04.MD.05**Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. Understand concepts of angle measurement.- MAT-04.MD.05.a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles.
- MAT-04.MD.05.b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

**MAT-04.MD.06**Measure angles in whole-number degrees using a protractor. using a protractor and ruler, Draw angles of a specified measure.**MAT-04.MD.07**Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

### MAT-04.G Domain:

**MAT-04.G.01**Draw and label points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.**MAT-04.G.02**Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of specified size. Recognize right triangles as a category, and Identify right triangles**MAT-04.G.03**Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures. Draw lines of symmetry.

### A Sample of What Your Child Will Be Working on in Grade 04

- Using whole-number arithmetic to solve word problems, including problems with remainders and problems with measurements
- Adding and subtracting whole numbers quickly and accurately (numbers up to 1 million)
- Multiplying and dividing multi-digit numbers in simple cases (e.g., multiplying 1,638 × 7 or 24 × 17, and dividing 6,966 by 6)
- Understanding and applying equivalent fractions (e.g., recognizing that 1⁄4 is less than 3⁄8 because 2⁄8 is less than 3⁄8)

- Adding, subtracting, and multiplying fractions in simple cases (such as 2 3⁄4 − 1 1⁄4 or 3 × 5⁄8), and solving related word problems
- Understanding simple decimals in terms of fractions (e.g., rewriting 0.62 as 62⁄100)
- Measuring angles and finding unknown angles in a diagram